Problem: Determine the intercepts of the line. $ -4x+7y=3$ $x$ -intercept: $\Big($
Explanation: The $x$ -intercept of a graph is the point of intersection between the $x$ -axis and the graph. Since the $x$ -axis is also the line $y=0$, the $y$ -value of this point will always be $0$. The $y$ -intercept of a graph is the point of intersection between the $y$ -axis and the graph. Since the $y$ -axis is also the line $x=0$, the $x$ -value of this point will always be $0$. To find the $x$ -intercept, let's substitute $ y= 0$ into the equation and solve for $x$ : $\begin{aligned}-4x+7\cdot{0}&=3\\ -4x&=3\\ x&=-\dfrac{3}{4}\end{aligned}$ So the $x$ -intercept is $\left(-\dfrac{3}{4},0\right)$. To find the $y$ -intercept, let's substitute $ x= 0$ into the equation and solve for $y$ : $\begin{aligned}-4\cdot{0}+7y&=3\\ 7y&=3\\ y&=\dfrac{3}{7}\end{aligned}$ So the $y$ -intercept is $\left(0,\dfrac{3}{7}\right)$. In conclusion, The $x$ -intercept is $\left(-\dfrac{3}{4},0\right)$. The $y$ -intercept is $\left(0,\dfrac{3}{7}\right)$.